Abstract: A method is given by which the response of a rotating or non-rotating timoshenko beam can be determined, subjected to an accelerating fixed direction distributed surface force. The beam model includes the gyroscopically induced displacement transverse to the direction of the load. The solution for pinned supports is set up using multi-integral transforms, and the inversion is expressed in terms of convulution integrals. These are numerically integrated for a uniformly distributed load having an exponentially varying velocity function. Results are presented for the displacement under the load's center as a function of position and for the displacement of every point on the beam at an instant in time. Comparisons are made between the beam response to a constant velocity load and its response to a load which accelerates to the same velocity.